In many surveys, multiple observations on the dependent variable are collected from a given respondent. The resulting pooled data set is likely to be censored and to exhibit cross-sectional heterogeneity. We propose a model that addresses both issues by allowing regression coefficients to vary randomly across respondents and by using the Geweke-Hajivassiliou-Keane simulator and Halton sequences to estimate high-order probabilities. We show how this framework can be usefully applied to the estimation of power outage costs to firms using data from a recent survey conducted by a U.S. utility. Our results strongly reject the hypotheses of parameter constancy and cross-sectional homogeneity.